Retirement
Annuity: Definition, Formula and Example
In finance mathematics, an annuity is a series of equally spaced payments; an insurance annuity is a contract that may provide income under specified terms.
Scope: General financial concept; examples are hypothetical.
Other names and related labels: Annuity cash flow; Insurance annuity.
How it works
An ordinary annuity pays at period end; an annuity due pays at period beginning. A mathematical payment stream can last for a fixed term. Lifetime insurance income also depends on mortality assumptions, contract options, charges and the insurer’s ability to pay.
Ordinary-annuity present value = payment × [1 − (1 + rate)^−periods] / rate
Use the rate per payment period. At zero interest, present value equals payment × number of payments. This formula alone is not a lifetime insurance quote.
Three year-end payments of $1,000
Discount each payment at 5% per year.
- Present value = $1,000/1.05 + $1,000/1.05² + $1,000/1.05³.
- The three present values sum to about $2,723.248.
The payment stream has a present value of $2,723.25 at the stated rate.
Exactly three fixed payments; no survival condition, tax, fees or surrender charge.
Try these example inputsA payment formula does not capture a whole insurance contract
A fixed-term payout can exhaust its balance. A lifetime payout may include survivor benefits or a guarantee period. Compare contract-specific fees, surrender terms and inflation protection rather than treating all products labeled annuities as equivalent.
Explore with a calculator
- Annuity Calculator
Project a hypothetical accumulation balance, not an insurer’s quote.
- Annuity Payout Calculator
Model a fixed-term payout or depletion horizon.
- Present Value Calculator
Discount an ordinary annuity or annuity due.
Sources and checks
Definition and example arithmetic checked . Sources explain the concepts; numerical examples use the assumptions stated above.
Calculation methodology and review status · All glossary terms